Initial Problem

Start: eval_textbook_ex1_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_textbook_ex1_bb0_in, eval_textbook_ex1_bb1_in, eval_textbook_ex1_bb2_in, eval_textbook_ex1_bb3_in, eval_textbook_ex1_start, eval_textbook_ex1_stop
Transitions:
t₁: eval_textbook_ex1_bb0_in(X₀, X₁, X₂) → eval_textbook_ex1_bb1_in(X₀, X₁, X₀)
t₂: eval_textbook_ex1_bb1_in(X₀, X₁, X₂) → eval_textbook_ex1_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₃: eval_textbook_ex1_bb1_in(X₀, X₁, X₂) → eval_textbook_ex1_bb3_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂
t₄: eval_textbook_ex1_bb2_in(X₀, X₁, X₂) → eval_textbook_ex1_bb1_in(X₀, X₁, 1+X₂)
t₅: eval_textbook_ex1_bb3_in(X₀, X₁, X₂) → eval_textbook_ex1_stop(X₀, X₁, X₂)
t₀: eval_textbook_ex1_start(X₀, X₁, X₂) → eval_textbook_ex1_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location eval_textbook_ex1_bb3_in

Found invariant X₀ ≤ X₂ for location eval_textbook_ex1_bb1_in

Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_textbook_ex1_bb2_in

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location eval_textbook_ex1_stop

Problem after Preprocessing

Start: eval_textbook_ex1_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_textbook_ex1_bb0_in, eval_textbook_ex1_bb1_in, eval_textbook_ex1_bb2_in, eval_textbook_ex1_bb3_in, eval_textbook_ex1_start, eval_textbook_ex1_stop
Transitions:
t₁: eval_textbook_ex1_bb0_in(X₀, X₁, X₂) → eval_textbook_ex1_bb1_in(X₀, X₁, X₀)
t₂: eval_textbook_ex1_bb1_in(X₀, X₁, X₂) → eval_textbook_ex1_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂
t₃: eval_textbook_ex1_bb1_in(X₀, X₁, X₂) → eval_textbook_ex1_bb3_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₄: eval_textbook_ex1_bb2_in(X₀, X₁, X₂) → eval_textbook_ex1_bb1_in(X₀, X₁, 1+X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁
t₅: eval_textbook_ex1_bb3_in(X₀, X₁, X₂) → eval_textbook_ex1_stop(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₀: eval_textbook_ex1_start(X₀, X₁, X₂) → eval_textbook_ex1_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂: eval_textbook_ex1_bb1_in(X₀, X₁, X₂) → eval_textbook_ex1_bb2_in(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• eval_textbook_ex1_bb1_in: [1+X₁-X₂]
• eval_textbook_ex1_bb2_in: [X₁-X₂]

MPRF for transition t₄: eval_textbook_ex1_bb2_in(X₀, X₁, X₂) → eval_textbook_ex1_bb1_in(X₀, X₁, 1+X₂) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

• eval_textbook_ex1_bb1_in: [1+X₁-X₂]
• eval_textbook_ex1_bb2_in: [1+X₁-X₂]

All Bounds

Timebounds

Overall timebound:2⋅X₀+2⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁+1 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀+2⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁+1 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₀+X₁+2 {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 3⋅X₀+X₁+2 {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₀+X₁+2 {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: 3⋅X₀+X₁+2 {O(n)}